Cart-Items Across Devices
When customers click through your emails to go back to your site's cart, the cookies enabled on your site are responsible for remembering those items. Now, if the customer shops on your site with one device, then return to the cart on a different device, the site will show an empty cart. This happens because the data remembering the cart-items (cookies) are stored on the device itself.
Cross-device tracking is possible but requires the Tokenization of the customer. Each customer will need to be assigned a specific ID (token) and all their cart information saved in a database. That information can then be grabbed by CartStack and inserted into the email template which would route customers back to their unique cart. Tokenization would require significant set-up if not already in place.
To find out if your site is capable of this, you can email your ecomm provider and ask if cart-items are saved to a database.